منابع مشابه
Uniqueness of large solutions
Given a nondecreasing nonlinearity f , we prove uniqueness of large solutions to the equation (1) below, in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex.
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This paper is about the evolution of a temperature front governed by the surface quasi-geostrophic equation. The existence part of that program within the scale of Sobolev spaces was obtained by the third author (2008). Here we revisit that proof introducing some new tools and points of view which allow us to conclude the also needed uniqueness result.
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It follows from a theorem of Veretennikov [4] that (1) has a unique strong solution, i.e. there is a unique process x(t), adapted to the filtration of the Brownian motion, satisfying (1). Veretennikov in fact proved this for a more general equation. Here we consider a different question, posed by N. V. Krylov [2]: we choose a Brownian path W and ask whether (1) has a unique solution for that pa...
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We study a nonlinear ltering problem in which the signal to be estimated is conditioned by the Wiener process in the observation equation. The main results establish pathwise uniqueness for the unnormalized lter equation and uniqueness in law for the normalized and unnormalized lter equations. 1 Introduction An early work on uniqueness for the stochastic di erential equations of nonlinear lteri...
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We prove that the weak solution of the Cauchy problem for the KleinGordon-Zakharov system and for the Zakharov system is unique in the energy space for the former system, and in H×L for the latter system, in dimensions three or lower. These are the largest Sobolev spaces (in three dimensional case) where the local wellposedness has been proven so far. Our proof uses an infinite iteration, where...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.05.085